Question

40 point question ....... pls urgent

Answer 1

The area swept by the minute hand in 12 minutes is 181.58 cm²

Step-by-step explanation:

In the circle clock

• The circumference of the circle is divided into 12 equal arcs
• The central angle of each arc is 30°, because the measure of the circle is 360° and divided by 12
• The central angle between each two consecutive hours is 30°
• There are 5 minutes between each two consecutive hours, then the central angle between each two consecutive minutes is 6° because 30° ÷ 5 = 6°
• When the minute hand is moved than the radius of the circle is the length of the minute hand
• When the hour hand is moved than the radius of the circle is the length of the hour hand

∵ The minute hand is swept by 12 minutes

∵ The central angle between each two consecutive minutes = 6°

∴ The central angle when the minute hand swept 12 minutes =

   6 × 12 = 72°

∵ The area of a sector of a circle = $\frac{x}{360}*\pi r^{2}$ ,

   where r is the radius of the circle and x is the central angle of

   the sector

∵ The radius of the circle is the length of the minute hand

∵ The minute hand in a clock is 17 cm long

∴ r = 17 cm

∵ The measure of the central angle is 72°

∴ x = 72°

- Substitute these values in the rule of the area of a sector

∵ Area = $\frac{72}{360}*\pi (17)^{2}$

∴ Area = 181.58 cm²

The area swept by the minute hand in 12 minutes is 181.58 cm²

Learn more:

You can learn more about the area of the sector in brainly.com/question/3456442

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